Response, wave function

As s starting point of our consideration, we rewrite (6) in terms of the linear response wave function (the reduced atomic system of units, h = e2 = m = 1,... 

Response, wave function, 242 Thomas-Fermi (TF), Thomas-Fermi-Dirac Variational Principle, 407... 

Reaction coordinate, 296, 314, 365, 368 Reaction Path (RP) methods, 390 Reaction surface, 390 Reaction volume, 390 Redundant variables, 34, 327 Relaxation time, in simulations, 380 Renormalized Davidson correction, 137 Resonance, resonance structures, 200 Response, wave function, 242 Restricted Active Space Self-Consistent Field (RASSCF) method, 119 Restricted Hartree-Fock (RHF) method, 70 Restricted Open-shell Hartree-Fock (ROHF) method, 70... 

Luce T A and Bennemann K H 1998 Nonlinear optical response of noble metals determined from first-principles electronic structures and wave functions calculation of transition matrix elements P/rys. Rev. B 58 15 821-6... 

Olsen J and J0rgensen P 1995 Time-dependent response theory with applications to self-consistent field and multiconfigurational self-consistent field wave functions Modern Electronic Structure Theory vo 2, ed D R Yarkony (Singapore World Scientific) pp 857-990... 

A second issue is the practice of using the same set of exponents for several sets of functions, such as the 2s and 2p. These are also referred to as general contraction or more often split valence basis sets and are still in widespread use. The acronyms denoting these basis sets sometimes include the letters SP to indicate the use of the same exponents for s andp orbitals. The disadvantage of this is that the basis set may suffer in the accuracy of its description of the wave function needed for high-accuracy calculations. The advantage of this scheme is that integral evaluation can be completed more quickly. This is partly responsible for the popularity of the Pople basis sets described below. 

For variationally optimized wave functions (HF or MCSCF) there is a 2n -I- 1 rule, analogous to the perturbational energy expression in Section 4.8 (eq. (4.34)) knowledge of the Hth derivative (also called the response) of the wave function is sufficient for... 

The Lagrange technique may be generalized to other types of non-variational wave functions (MP and CC), and to higher-order derivatives. It is found that the 2n - - 1 rule is recovered, i.e. if the wave function response is known to order n, the (2n + l)th-order property may be calculated for any type of wave function. 

Although a calculation of the wave function response can be avoided for the first derivative, it is necessary for second (and higher) derivatives. Eq. (10.29) gives directly an equation for determining the (first-order) response, which is structurally the same as eq. (10.36). For an HF wave function, an equation of the change in the MO coefficients may also be formulated from the Hartree-Fock equation, eq. (3.50). 

The first term is the Hellmann-Feynman force and the second is the wave function response. The latter now contains contributions both from a change in basis functions and MO coefficients. 

The correlation of electron motion in molecular systems is responsible for many important effects, but its theoretical treatment has proved to be very difficult. Thus many quantum valence calculations use wave functions which are adjusted to optimize kinetic energy effects and the potential energy of interaction of nuclei and electrons but which do not adequately allow for electron correlation and hence yield excessive electron repulsion energy. This problem may be subdivided into cases of overlapping and nonoverlapping electron distributions. Both are very important but we shall concern ourselves here with only the nonoverlapping case. 

Sales response to advertising, 265 Salpeter, E. E641 Sample, adequacy of, 319 Sampling theorem, 245 Scalar product of two wave functions, 549,553... 

J. Olsen and P. Jorgensen. Time-Dependent Response Theory with Applications to Self-Consistent Field and Multiconfigurational Self-Consistent Field Wave Functions, in Modern Electronic Structure Theory, edited by D. R. Yarkony, volume 2, chapter 13, pp. 857-990. World Scientific, Singapore, 1995. 

The simplified theory allows the time-dependent wave function to be calculated rapidly for any specified laser field. However, controlling the dynamics of the charge carriers requires the answer to an inverse question [18-22]. That is, given a specific target or objective, what is the laser field that best drives the system to that objective Several methods have been developed to address this question. This section sketches one method, valid in the weak response (perturbative) regime in which most experiments on semiconductors are performed. 

Dickson and Becke, 1996, use a basis set free numerical approach for obtaining their LDA dipole moments, which defines the complete basis set limit. In all other investigations basis sets of at least polarized triple-zeta quality were employed. Some of these basis sets have been designed explicitly for electric field response properties, albeit in the wave function domain. In this category belong the POL basis sets designed by Sadlej and used by many authors as well as basis sets augmented by field-induced polarization (FTP) func-... 

The complex scattering wave function can be specified by nodal points at which u = 0,v = 0. They have great physical significance since they are responsible for current vortices. We have calculated distribution functions for nearest distances between nodal points and found that there is a universal form for open chaotic billiards. The form coincides with the distribution for the Berry function and hence, it may be used as a signature of quantum chaos in open systems. All distributions agree well with numerically computed results for transmission through quantum chaotic billiards. 

In band theory the electrons responsible for conduction are not linked to any particular atom. They can move easily throughout the crystal and are said to be free or very nearly so. The wave functions of these electrons are considered to extend throughout the whole of the crystal and are delocalized. The outer electrons in a solid, that is, the electrons that are of greatest importance from the point of view of both chemical and electronic properties, occupy bands of allowed energies. Between these bands are regions that cannot be occupied, called band gaps. 

It is worth noting that screened response x/C r ) can be computed from the Kohn-Sham orbital wave functions and energies using standard first-order perturbation theory [3]... 

A wave is described by a wave function y(f, /), either scalar (as pressure p) or vector (as u or v) at position r and time t. The wave function is the solution of a wave equation that describes the response of the medium to an external stress (see below). 

One of the main limitations of the experimental methodology described above is related to the time constraint. It hinders the study of many interesting reactions that are too slow to ensure that the amplitude of the photoacoustic wave is independent of the kinetics of the process. This is the case, for instance, of transient lifetimes in the range of 100 ns to 0.1 ms for a 0.5 MHz transducer. Fortunately, there is an alternative procedure to deal with those cases where the condition r 1/v does not hold. The procedure, known as time-resolved PAC (TR-PAC), was developed by Peters and co-workers [282,284,299] and considers that the observed wave, Sexp(t), reflects the kinetics of the true heat deposition, S(t), as well as the detector response wave, T(t). In other words, SexP(t) is the convolution of S(t) with the transducer function, T(t)... 

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